The evolution of death rates and life expectancy in Denmark

From 1835 to date Denmark has experienced an increase in life expectancy at birth of about 40 years for both sexes. Over the course of the last 170 years, life expectancy at birth has increased from 40 to 80 years for women and from 36 to 76 years for men, and it continues to rise. Using a new methodology, we show that about half of the total historic increase can be attributed to the sharp decline in infant and young age death rates up to 1950. However, life expectancy gains from 1950 to date can be primarily attributed to improvements in the age-specific death rates for the age group from 50 to 80, although there is also a noticeable contribution from the further decline in infant mortality over this period. With age-specific death rates up to age 60 now at a very low absolute level, substantial future life expectancy improvements must necessarily arise from improvements in age-specific death rates for ages 60 and above. Using the developed methodology, we quantify the impact of further reductions in age-specific mortality. Despite being one of countries with the highest life expectancy at the beginning of the 20th century, and despite the spectacular historic increase in life expectancy since then, Denmark is, in fact, lagging behind compared to many other countries, notably the other Nordic countries. The main reason is an alarming excess mortality for cause-specific death rates related to ischaemic heart diseases and, in particular, a number of cancer diseases. Age-specific death rates continue to improve in most countries, and a likely scenario is that in the future Denmark will experience improvement rates at the international level or perhaps even higher as a result of a catch-up effect.     

Life Expectancy in 2040: What Do Clinical Experts Expect?

We use expert clinical and public health opinion to estimate likely changes in the prevention and treatment of important disease conditions and how they will affect future life expectancy. Focus groups were held including clinical and public health faculty with expertise in the six leading causes of death in the United States. Mortality rates and life tables for 2040 were derived by sex and age. Life expectancy at age 20 and 65 was compared to figures published by the Social Security Administration and to estimates from the Lee-Carter method. There was agreement among all three approaches that life expectancy at age 20 will increase by approximately one year per decade for females and males between now and 2040. According to the clinical experts, 70% of the improvement in life expectancy will occur in cardiovascular disease and cancer, while in the last 30 years most of the improvement has occurred in cardiovascular disease. Expert opinion suggests that most of the increase in life expectancy will be attributable to the already achieved reduction in smoking rates, especially for women.     

Modeling disease elimination

The effect of the elimination of mortality from heart disease and cancer was modelled mathematically to allow for the effect of other competing causes of death. The model allows for potential dependence between heart disease or cancer and other causes of death by using cupola functions, which analyse the individual risk itself and the dependence structure between causes of death by using correlation coefficients. As the strength of these risk associations is unknown, the study investigated both full positive and negative dependence and compared this with no dependence. Depending upon the degree and type of correlation assumed, positive or negative, the life expectancy at birth is increased by between 3 months and 6.5 years if cancer mortality was eliminated, and between 5 months and 7.5 years in the case of heart disease. In addition, estimates of these effects on life insurance premia can be made with the greatest reduction for women with the elimination of cancer mortality. These figures provide a range of improvements in life expectancy and the consequent effect on life insurance risk premium rates which elimination of either of these important diseases would produce.     

Der Einfluss des demographischen Wandels auf die Ausgaben der Krankenversicherung

The analysis presented in this document investigates the question of whether the increase in life expectancy causes financial stress for health insurance systems or not. In particular, the authors focused on the financial impact of the ?costs of dying“ and how much these costs contribute to the total health costs. The article analyses an in-patient and an out-patient tariff of a large private health insurance company in Germany. It is based on health care costs of people who died in 1999 and of those who continued to live. The percentage of the costs of dying is often overestimated. However, the costs of those who continued to live increased overproportionately. In particular, this was true for the insured people over 80 years.The claim that the increase of life expectancy only postpones the high costs in the future and has no impact on the financial conditions of health insurance is doubtful. Older people live longer and have more opportunity to take medication and receive therapy for a longer period. Therefore we argue that longer life expectancy and other factors like progress in medical technology pose a severe threat on the financial stability of health insurance.     

Demographic change, social security systems, and savings

In theory, improvements in healthy life expectancy should generate increases in the average age of retirement, with little effect on savings rates. In many countries, however, retirement incentives in social security programs prevent retirement ages from keeping pace with changes in life expectancy, leading to an increased need for life-cycle savings. Analyzing a cross-country panel of macroeconomic data, we find that increased longevity raises aggregate savings rates in countries with universal pension coverage and retirement incentives, though the effect disappears in countries with pay-as-you-go systems and high replacement rates.     

Langlebigkeit und Altern: Gene oder Umwelt?

Aging is defined as loss of homeostasis which affects all metabolic systems, including DNA. Interspecies comparisons and lessons from the human genetic instability syndromes suggest a correlation between DNA-homeostasis and maximum lifespan, whereas average lifespan depends mainly on environmental factors. Current demographic data suggest a maximum lifespan in humans of 110–115. The average life expectancy at birth has reached 80 years in the wealthy nations and may exceed, at least in females, 90 years by the year 2050. Genetic and biological reasons, but also lifestyle factors, account for the greater longevity of women. Attempt to define a ?longevity“ genotype so far have not been met with success, but carriers of the ApoE4-Allele appear to have a disadvantage. Unlike the situation in model organisms, aging and longevity in humans seem to be influenced by numerous genes and environmental interactions. Most people do not die of old age but of age-related diseases which are frequent because of lack of natural selection against genetic defects that cause late-onset diseases. Moreover, genes causing late-onset diseases show evidence of antagonistic pleiotropy, rendering these genes resistant to removal from our genome. Likewise, thermoinstability of DNA and generation of reactive oxygen species during oxidative phosphorylation are two endogenous sources of genomic instability that limit our lifespan and cannot be overcome without fundamentally altering the biological make-up of our species. Genomic instability causes cancer and accelerates the aging process, as evidenced by the human caretaker gene syndromes which typically show progeroid features. From a genetic point of view, cancer and aging may be moderately delayed and / or mitigated by lifestyle and medical / environmental interventions, but given the constraints of our biological make-up, they cannot be eradicated.     

How long might the younger-old live: A predictive model

Life expectancy amongst older people in industrialised countries has been improving over an extended period and still continues to do so. This has ramifications for providers of services to this population, thus necessitating a level of forward planning. Predictive models of remaining life expectancy for older age groups can assist long-term planning processes. This paper presents an extrapolative approach to forecasting remaining life expectancy. Based on logistic modelling of historic mortality and survivorship for the “younger-old” male population of England and Wales over the period 1970-2005, a parsimonious two-parameter model is derived. This model provides a close correspondence to published period life table data. Trends in these parameters are then fitted and extrapolated to enable projections of life expectancy up to 40 years into the future. Alternative assumptions are used to determine a range of future life expectancy trajectories for a 65-year-old male. Occupational pension scheme provision is identified as an area of particular concern in the context of increasing longevity. As an illustration, the life expectancy trajectories are combined with differing discount rate assumptions to generate a number of alternative pension liability scenarios for the extrapolation period.     

Gender Convergence in Human Survival and the Postponement of Death

It has been a long-accepted demographic maxim that females outlive males. Using data for England and Wales, we show that life expectancy at age 30 is converging, and continuation of this long-term trend suggests life expectancy could reach parity in 2030, resulting in considerable economic and social ramifications. The degree of parity in life expectancy is examined by comparing the historical record in four countries that show that convergence is not a new phenomenon. Contributory factors are considered including changes in male smoking habits and male employment patterns. A model is presented that considers gender differences in longevity using novel methods for analyzing life tables. It determines the ages from which death is being postponed, to the ages at which people now die, the relative speed at which these changes are taking place between genders, and how the changes observed are affecting survival prospects at different ages up to 2030. It finds that as life expectancy continues to rise there is accompanying convergence in modal age of death of between 92 and 93 years.     

延迟退休年龄、内生生育率与养老金

本文通过构建内生生育率的OLG模型,从微观视角考察了延迟退休年龄对生育率、养老金替代率及其个人养老金收入的影响。研究表明:(1)延迟退休年龄会提高均衡时的生育率水平,但提高幅度非常有限。(2)生育率的提高会增加未来劳动力供给,促进养老金替代率上升和养老金收入增加,而延迟退休年龄延长了养老保险缴费期限,也会促进养老金替代率上升和养老金收入增加;但同时,延迟退休年龄将使得预防性储蓄下降,资本积累降低,工资收入下降,养老金收入降低。因此,延迟退休年龄会使养老金替代率上升。当资本产出弹性大于或等于0.5时,延迟退休年龄会使得养老金收入降低;当资本产出弹性小于0.5时,在平均预期寿命较大或养老保险缴费比例较高的情形下,养老金收入会随着退休年龄的延迟而增加,反之,其会随着退休年龄的延迟而降低。进一步地,将模型拓展到包含人力资本的情形,延迟退休年龄仍会提高均衡时的生育率与养老金替代率。     

Estimating mortality rates: the role of proportional life expectancy

The computation of long-term survival is usually based on adjustments to the conventional life table. Assessing the validity of different types of adjustments can be difficult, partly because of the need to allow for two age-related trends-the decline in the average (normal) life expectancy, as well as in the new (abnormal) estimate. In this paper, we illustrate the value of routinely expressing each new estimate as a percentage of normal at each age. An additional finding has been that in some common disorders this proportional life expectancy (PLE) remains remarkably constant over many years.     

Minimum Death Rates and Maximum Life Expectancy: The Role of Concordant Ages

Only five populations have achieved maximum life expectancy (or best practice population) more than occasionally since 1900. The aim of this article is to understand how maximum life expectancy is achieved in the context of mortality transition. We explore this aim using the concepts of potential life expectancy, based on minimum rates at each age among all high longevity populations, and concordant ages. Concordant ages are defined as ages at which the minimum death rate occurs in the population with the maximum life expectancy. The results show the extent to which maximum life expectancy could increase through the realization of demonstrably achievable minimum rates. Concordant ages are concentrated at increasingly older ages over time, but they have produced more than half of the change in maximum life expectancy in almost all periods since 1900. This finding is attributed to their quantity and position whereby concordant ages are concentrated at the ages that have the greatest impact on mortality decline in a particular period. Based on mortality forecasts, we expect that concordant ages will continue to lead increases in female maximum life expectancy, but that they will play a weaker role in male maximum life expectancy.     

Estimation of future mortality rates and life expectancy in chronic medical conditions

Estimates of old-age mortality are necessary for the construction of life tables and computation of life expectancy, and are essential in the growing area of life insurance for the elderly. Two common assumptions are that either the excess death rate (EDR) or the relative risk (RR) stays constant with increasing age. It is known, however, that for most medical conditions the former underestimates the risk and the latter overestimates it. A third popular method is that of rating up: a subject is said to be "rated up k years" if his future mortality rates are assumed to be those of a person in the general population who is k years older. It is shown here that this method generally leads to gross overestimates of old-age mortality. We consider two less-commonly used models, log-linear declining relative risk (LDR) and constant proportional life expectancy (PLE), and compare them to the methods of constant EDR, constant RR and rating up. Although slightly more complicated to employ than the other methods, both LDR and PLE generally give better estimates of mortality and life expectancy. When mortality rates for chronic conditions are known within a certain age range, and estimates outside of the range are required, the LDR and PLE methods may be preferable to the more familiar methods of constant EDR, constant RR, or rating up.     

Firm life expectancy and the heterogeneity of the book-to-market effect

I argue that the reason the book-to-market effect is stronger in small stocks is because smaller stocks generally have shorter life expectancy and therefore shorter equity duration. I build a model in which the book-to-market effect is stronger in stocks with shorter life expectancy. Empirically, I use delisting probability as my proxy for life expectancy. The data support my model's central prediction and its additional implications for stock return and variance. My results provide a rational explanation for the heterogeneity of the book-to-market effect, evidence previously taken as support for behavioral explanations.     

How to prepare a life expectancy report for an attorney in a tort case

The purpose of this methodology article is to describe a suitable format for a legally acceptable report on the life expectancy of the principal in a tort case that is being advocated or defended by an attorney. Life insurance medical directors and underwriters are clearly skilled and experienced in mortality risk classification for life insurance. However, the judicial system is accustomed to measuring excess mortality only in terms of reduced life expectancy. The analyst preparing the report must convert the excess mortality into a figure for reduced life expectancy and compare this with the life expectancy of persons matched by age, sex and race in the latest Decennial US Life Tables. This process is different from the life insurance underwriting process. A life table projected to age 109 must be constructed as an essential part of the report, and the entire process must be presented clearly and convincingly. There are good reasons why the excess death rate (EDR) should be used as the index of excess mortality in constructing the life table, in preference to the mortality ratio (MR), which is used most of the time in life insurance risk classification. All of these considerations are discussed in this article, which is based on a sample of 40 cases handled by the author, a retired life insurance medical director.     

Effects of Health and Longevity on Financial Risk Tolerance

We investigate the effects of health and life expectancy on tolerance of financial risk. Using a standard life-cycle model, we find that the effects of health and life expectancy on preferences over lifetime-income risk are theoretically ambiguous. However, risk tolerance is independent of health and life expectancy when utility takes one of the standard (harmonic absolute risk aversion) functional forms or when optimal consumption is constant over time. Our empirical results, using data from a stated-preference survey (n=2,795), suggest that financial risk tolerance is positively associated with both health and life expectancy; hence utility is not consistent with standard functional forms.     

Life expectancy--a commentary on this life table variable

In 1992, I wrote an article on a method of modifying the Decennial US Life Table to accommodate any pattern of excess mortality expressed in terms of excess death rate (EDR), for the specific purpose of calculating the reduced life expectancy, e. I believe this was the first article published in the Journal of Insurance Medicine (JIM) that dealt specifically with life expectancy as an index of survival and risk appraisal, never used in the classification of extra mortality risk in applicants for life insurance. In this commentary, I discuss the 1989-91 US Decennial Life Table in detail. I link the subject matter of the 1992 article with several more recent articles that also focus on the utility of life expectancy in underwriting structured settlement annuities and preparing reports on life expectancy for an attorney in a tort case. A few references are given for further reading on life table methodology and its use in the most accurate estimate of life expectancy, given the inherent limitations of the life table and the limited duration of follow-up studies.     

预期寿命对中国养老保险支出的影响效应——基于省级面板数据的实证分析

利用1995—2014年我国31个省份的省级面板数据实证检验了预期寿命延长对我国养老金支出的影响效应。结果发现：人口平均预期寿命对我国养老金支出水平具有显著的正向影响。实证结果显示：研究样本期间内人口平均预期寿命的增加导致了我国养老金支出水平增加了0.94个百分点,对养老金支出水平增加的贡献度高达76%,成为了我国养老金支出增加的主导因素。随着我国人口预期寿命延长模式逐渐进入到以老年人口死亡率下降为主导,这种人口增龄效应对养老金支出的影响还会进一步增强和深入,在未来养老保险制度改革优化过程中需对预期寿命这一因素加以重点关注。     

人口预期寿命与经济增长关系的研究评述

随着人口经济学理论的发展和OLG模型的不断拓展,关于预期寿命与经济增长关系的理论研究与实证分析逐渐深入。由于研究视角、理论模型以及样本数据等方面的不同,学者们关于两者关系的观点存在较大差异。本文梳理了部分国外当前主要相关文献,认为目前关于预期寿命作用于经济增长的观点可以归纳为:人口预期寿命上升提高人力资本回报率和储蓄率,进而促进经济增长;人口预期寿命上升将导致人口增长,进而降低人均GDP增长;人口预期寿命与经济增长存在非线性关系,非线性特征取决于人口结构转型、初始预期寿命等因素。     

Pricing implications of trends in population mortality and underwriting effectiveness

Pricing actuaries try to anticipate insured lives mortality rates for decades into the future by considering historic relationships between population and insured lives mortality and trends in population mortality. The degree to which underwriting might decrease insured lives mortality relative to population mortality is of particular importance. A comparison of trends in population and insured mortality is presented to illustrate historic relationships. Two theories for future life expectancy trends are: 1) no foreseeable limit to life expectancy, and 2) life expectancy limited by biological forces. Factors that may increase or decrease the future effectiveness of underwriting are reviewed.     

我国养老保险个人账户给付期研究——基于平均余命视角

依据平均余命可以测算出养老保险个人账户超支月数,由个人账户超支月数可以判断养老保险个人账户给付期的合理性。通过对城镇职工养老保险制度、城镇居民养老保险制度和新型农村养老保险制度个人账户超支的测算,发现中国城乡居民平均余命延长导致养老保险个人账户存在超支,并且个人账户超支存在明显的性别差异和城乡差异的特点,说明中国养老保险个人账户给付期设计不合理。建议按照平均余命设计差异的养老保险个人账户给付期。